One of the goals in basic biological and social research is to measure the empirical relationship between variables that have certain theoretic relationships. However, this objective is often limited by the fact that certain variables (e.g., health, social status, economic status, physical strength) that dominate our theoretic statements are complex and abstract and cannot be operationalized fully in terms of a single empirical measurement. Suppose we are trying to estimate the relationship between two (or more) abstract variables which cannot be measured directly, and multiple empirical indicators are available for each abstract variable. Furthermore, suppose an auxillary theory is available which imposes constraints on the relationships between each abstract variable and its empirical indicator. The purpose of the proposed project is to analyze how the multivariate relationships between the empirical indicators of each abstract variable and the auxillary theory can be used to estimate the relationship between the abstract variables. The problem of testing the significance of this relationship will also be examined. Procedures have been devised (Costner (1960), Mayer and Younger (1974) for estimating and testing the relationship between abstract variables given empirical indicators provided the auxillary theory dictates that the empirical indicators are linearly related to the abstract variables (except for random disturbances). Using previous work of the Principal Investigator, attention will be focused on the problems of estimation and testing when auxillary theory dictates that the empirical indicators are (at best) monotonically related to the abstract variables.